I leave mine on the counter for a couple of days, in a dixie cup, then put them in a baggie, without a paper towel, and stick them in the crisper drawer. A paper towel probably wouldn't hurt, but shouldn't be needed, if they are dry. I've never had one sprout, that I can remember, so they must have been dry enough when I put them in the fridge.
You're going to find many ways to germinate them, and you'll need to find what works best for you. I always germinate mine in the fridge, but others take them out of the fridge. Some moisture is needed for that step, and I always use peroxide and water, but not everyone does that. There are lots of threads here where people discuss their method for germination. Other people just stick them in the ground, or in potting mix, and let them do their thing.
